Commun. Comput. Phys., 5 (2009), pp. 1012-1029.


A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models

Xianliang Hu 1, Ruo Li 2*, Tao Tang 3

1 Department of Mathematics, Zhejiang University, Hangzhou 31027, China; and Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA 91125, USA.
2 CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China.
3 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong.

Received 2 April 2008; Accepted (in revised version) 3 August 2008
Available online 20 October 2008

Abstract

In this work, we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of the relevant dependent variables, namely the thermal field function and the phase field function, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.

AMS subject classifications: 65M20, 65N22, 80A22

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Key words: Multi-mesh, local refinement, adaptive finite element, phase field.

*Corresponding author.
Email: huxl98@yahoo.com.cn (X. Hu), rli@math.pku.edu.cn (R. Li), ttang@math.hkbu.edu.hk (T. Tang)
 

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